Hidden strange metallic state in underdoped electron-doped cuprates

The low-temperature linear-in-T resistivity of “strange metals,” such as the metallic state of the cuprate high-temperature superconductors, has long been thought to be associated with a quantum critical point. However, recent transport studies of the cuprates have found this behavior persists over a finite range of overdoping. In this work, we report magnetoresistance and Hall effect results for electron-doped films of the cuprate superconductor ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ (LCCO) for temperatures from 0.7 to 45 K and magnetic fields up to 65 T. For $x=0.12$ and 0.13, just below the Fermi surface reconstruction (FSR) at $x=0.14$, the normal state in-plane resistivity exhibits a well-known upturn at low temperature. Our new results show that this resistivity upturn is eliminated at high magnetic field and the resistivity becomes linear-in-temperature from ∼40 K down to 0.7 K. The magnitude of the linear coefficient scales with Tc and doping, as found previously [K. Jin, Nature(London) 476, 73 (2011), T. Sarkar, Sci. Adv. 5, eaav6753 (2019)] for dopings above the FSR. This striking observation suggests that the strange metal is not confined to a single “critical point” in the phase diagram, but rather is a robust universal feature of the metallic ground state of the cuprates.

Figure 1

Temperature dependent magnetoresistance (${\rho }_{xx}\left(T,H\right))$ of LCCO for $x=0.12$ (a) and 0.13 (b) ($H\perp ab$-plane). Black arrow indicates the increasing temperature direction from 0.7 to 44 K. (measured in 65 T pulsed field). In (c) and (d) the resistivity vs temperature is found from the (a) and (b) data, respectively. The $H^{*}($ the field where $T_m$ vanishes) are ∼60 T for $x=0.13$ and above 65 T for doping $x=0.12$.

Figure 2

(a) Transverse magnetoresistivity (${\rho }_{xx}\left(T,H\right)$) vs temperature of ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ for $x=0.15$ (data taken from Ref. [22]). The dotted lines are guides to the eye. (Inset) The resistivity minima ($T_m$) vs field. The $T_m$ is determined by taking the derivative of the dotted lines and $H^{*}$ is the field where $T_m$ vanishes. (b) Resistivity vs T at higher fields. The dotted lines are a linear fit with ${\rho }_{xx}\left(T,H\right)={\rho }_{xx}\left(0,H\right)+A\left(x\right)T$, with $A\left(x\right)=0.17$ (60 T), 0.19 (70 T), and $0.2\left(80\mathrm{T}\right)\mu \mathrm{\Omega }\mathrm{cm}{\mathrm{K}}^{-1}$. Field is applied along the $c$ axis for all data.

Figure 3

(a) Resistivity vs temperature for LCCO $\mathrm{x}=0.12$ at 65 T (black data points) and $\mathrm{x}=0.13$ at 60 T (blue data points) from 700 mK to 45 K. The red solid line is a fit to ${\rho }_{xx}\left(T,H\right)={\rho }_{xx}\left(0,H\right)+A\left(x\right)T$(b) Previous work is reported in Refs. [1, 2, 4]. Open circles [from (a)] and solid black circles (taken from Ref. [2]) are the slopes, $\left(A\left(x\right)\right)$, of the linear-in-T resistivity. The red circles are $T_c\left(x\right)$ normalized to the $T_c$ at the optimal doping (26 K). Dotted lines are guide to the eye.

Figure 4

(a) Hall coefficient vs field of LCCO for doping $x=0.13$ at various temperatures. (b) The Hall coefficient vs T as a function of field [data taken from (a)]. (c) Hall coefficient vs field of LCCO for doping $x=0.12$ at various temperatures. These data are found after subtracting any magnetoresistance component by measuring $R_{xy}$ in magnetic fields from +35 to −35 T.